Jazzed by a fourth-place finish in the New Hampshire primary, Republican presidential candidate Jeb Bush opened his campaign for the next contest in South Carolina by taking repeated shots at front-runner Donald Trump.

Mr. Bush accused the billionaire real estate mogul and reality TV star of being a divisive figure just like President Obama and slammed him for declaring bankruptcy four times for his business ventures.

“I’m giving you a reality-based answer not a realty-TV answer,” Mr. Bush told the crowd at a town hall in Bluffton, South Carolina, as he touted his record of cutting taxes, reining in spending and reforming state government as governor of Florida.

“Trump can talk a good game, and he’ll win. He’s a good talker,” Mr. Bush said in an uncharacteristically energetic speech. “We don’t need talkers. We need doers.”

He later jabbed Mr. Trump for his bankruptcy filings, which Mr. Trump has defended as smart business moves and taking advantage of U.S. bankruptcy laws.

“We don’t need a president who thinks it is a victory to go bankrupt,” Mr. Bush said.

Mr. Trump and Mr. Bush have clashed throughout the campaign, though Mr. Bush has trailed far behind the front-runner in almost every poll.

Mr. Trump, who won the New Hampshire primary by a large margin, frequently slams Mr. Bush for being a “low energy” person, a moniker that stuck to Mr. Bush and which the former governor appeared to be working hard to erase.

But Mr. Bush took heart at beating his former protege Sen. Marco Rubio of Florida, who has emerged as a top contender with Mr. Bush and other governors as the establishment alternative to Mr. Trump.

Mr. Trump leads in South Carolina with 39 percent, followed by Mr. Cruz at 19.7 percent, Mr. Rubio at 12.7 percent and Mr. Bush at 10 percent, according to the Real Clear Politics average of recent polls.